Posts Tagged ‘drops’

How can the addition of water vapor make it lighter? When I take a dishrag and wet it, it gets heavier; how can I take a parcel of air, add water, and thereby make it lighter? This is all nonsense!

(I suppose this lesson should have come before the one about phase change, but better late than never.)

Yes, if you add liquid water to a parcel of air it will be heavier, but humidity is not about liquid water; it is about water vapor. We confuse the two because a fog is obviously heavy and since the droplets in fog are so small as to be invisible, we think of them as vapor. This is an understandable mistake; we can’t see fog droplets and we understand that the air is saturated in a fog, so we think that the fog is the vapor. Besides, in poetry, fog is called vapor.

But for scientific purposes, (and in sci-speak) vapor has a specific meaning; and fog is not vapor.

Fog and cloud droplets, for all that they are very small, are enormous compared to a molecule of water – and true water vapor means water floating in molecular form. Fog forms when saturated air cools and some of the water condenses. The remaining air is still saturated, and would be so even if you took away all the water droplets. The saturation is about vapor, not about droplets, however tiny.

How big is a water molecule?

Can a water molecule really be much smaller than a cloud droplet?

If the water droplets of an evaporating fog are a few 1/100ths of a millimeter wide, they are still a good five orders of magnitude larger than a molecule of water which is a few Ångstroms wide. Five orders of magnitude… That means like the difference between a softball and a city; the difference between a single grain of dandelion pollen and your kitchen table; between a beetle and a freight train, between a kitten and a thunderhead. The difference is simply enormous.

Look closely at the steam coming out of your teapot. Notice that right by the spout, the steam is invisible. An inch or two away, it is white. Right out of the spout, it is vapor; a short distance away, it has condensed into tiny droplets.

Avogadro:

Now that we have an idea of what we mean by humid air – air full of water vapor – we can say something else which we learned from the research of a fellow named Avogadro and those who followed his lead; it is this:

Every parcel of gas, every volume of gas, holds the exact same number of molecules, no matter what kind of molecules they are. Well, that’s not quite right: of course a gas that is hotter expands and has fewer molecules in a specific volume; or a gas can have a wrapping around it such as a balloon and be squashed so more molecules fit into a specific volume. But if we have an imaginary box of gas of any precise size, then every other box of that size that has the same temperature and the same pressure has the same number of molecules, and it doesn’t matter whether the molecules are water, oxygen, nitrogen, carbon dioxide, or even much larger molecules such as vanillin or cinnamaldehyde. It will always be the same total number of molecules if the box size, the temperature, and the pressure are the same.

We don’t imagine this would be true, because we think of atoms and molecules as balls of different sizes, and we would certainly not get as many beach balls as we would marbles into any box. But the point about gases is that they are balls in motion, all banging against each other and bouncing away, and – this is the crucial point – the little ones move faster. Of course they move faster. Wouldn’t you move faster if a bear bumped into you as opposed to a rabbit or a fly? Because the little ones move faster, they effectively take up as much room as the big ones that move more slowly, and the sum of it is that a given volume of gas always has the same number of molecules. Some may be little speeding molecules that would condense into something quite small; others may be big galumphing ones that would condense into something moderately large. But if you count them, the number is the same.

And if you have 22.4 liters of cold gas down by the sea, you have precisely 6.02 x 1023 molecules in your box. That’s a famous number, called Avogadro’s number, and you can ask your chemistry teacher why they chose 22.4 liters instead of something more obvious. (There is always an interesting reason for such things.)

But always having the same number of molecules means that some gases are heavier than others. The heavy gases don’t take up any more room; they are just heavier. It follows that they are more gravity-challenged; they fall while others rise.

Saturated air rises:

So let us get back to the air with its water vapor. When water vapor gets mixed into the air, the oxygen and nitrogen have to move over to make room because only 6,02 x 1023 bits can fit into the box; ultimately, when you are out-of-doors, the gases move up, because all the space around is already filled with oxygen, nitrogen, argon, and the other components of air, and “up” is the only place where there is more room. But the water molecule is actually lighter than the oxygen molecule and also lighter than the nitrogen molecule.

Some airy weights:

Basically, you get the weight of a molecule by counting the protons and neutrons in its atoms:

That makes O2 have a weight of 16 + 16 = 32

It makes N2 have a weight of 14 + 14 = 28

Carbon dioxide (CO2) has a weight of 12 + 16 + 16 = 44

Argon is an atom that has a weight close to 40

Finally, water H2O has have a weight of 1 + 1 + 16 = 18

See how light the water is? It is amazing that it doesn’t float away altogether and become lost in space.

Anyway, you can see that a box of gas that is part water vapor will be lighter than one that is only oxygen and nitrogen. So it will rise.

In conclusion

When people talk about dry air soaking up water like a sponge, then, it’s not really like a sponge that gets heavier as it soaks up water. It’s more like potting soil that gets lighter (per cubic foot) as you add Styrofoam (or whatever that white stuff is). So saturated air – air holding all the water vapor it can – naturally rises.

I’ve been reading a new book — an old book really: From Raindrops to Volcanoes by Duncan Blanchard, first published in 1967 and presently being reprinted by Dover. It’s a kind of personal journal of Blanchard’s scientific adventures going from the study of how raindrops generate bubbles in the sea, to the way that these bubbles break and send tiny droplets into the air, to the possible relationship between these droplets and atmospheric charge, to the question of how undersea volcanoes send charges into the atmosphere.

This is the kind of book that shows you how scientists really think: An idea forms; in the course of checking that idea, other thoughts form and other experiments suggest still further avenues of thought. Along the way, other people have similar questions and sometimes more ingenious exercises to test them, and then, charmingly, a visit to the library unearths the works of men who raised these questions hundreds of years ago and made their own guesses, wise or foolish.

So, when a drop causes a bubble, and the breaking of the bubble causes the forceful ejection of new and incredibly tiny droplets into the air, how fast do you suppose that ejection really starts them off? It has to have some momentum because the air is quite thick compared to these tiny droplets and to get them up above the sea requires considerable force… The large ones, of course, we actually see; they might be traveling as fast as we swing our arms, and that can’t be much more than a few miles an hour, the speed at which we walk and swing our arms, right?

But would you believe 180 miles an hour for the little ones? No way! Please read his book and explain to me what he did wrong; there must be something. I didn’t follow every equation, I confess.

Actually, I am sure he was careful; and even though there are some math parts that will not catch everyone’s attention, he does give amazingly clear explanations of his work; it’s not just answers, but how he got there. He has the heart of a teacher; he wants to share his fascination with the physical world, all full of surprises.

Here is an image of volcanic lightning from another source. It’s the Chaiten Volcano in Chili, which erupted May of 2008. Notice that the cloud is black and smoky, not grey like a rain cloud. The picture is from a news outlet.